In order to attenuate rotational irregularities of an internal combustion engine crankshaft, principally at speeds between idle speed and an intermediate engine speed, for example approximately 2500 revolutions per minute, it has been proposed in the document FR2857073 to couple, directly to the crankshaft of an internal combustion engine, an inertial flywheel that attenuates torsional vibrations or rotational speed fluctuations, comprising two coaxial inertial masses, a first of which is rotationally integral with the crankshaft and has a starter ring gear and a reaction plate of a friction clutch, while the second is rotationally movable with respect to the first as a result of pivot-mounted connecting modules each having at least one oscillating arm that pivots with respect to the first inertial mass around an axis parallel to the axis of revolution; an oscillating mass positioned at a free end of the oscillating arm so as to be movable in an essentially radial direction; and a link connecting an intermediate point of the oscillating arm to the second inertial mass. Thanks to a centrifugal effect, the pivot-mounted modules resist the relative rotation of the inertial masses, exerting a return torque substantially proportional to the relative rotation of the two inertial masses and to the square of the rotation speed of the inertial mass connected to the crankshaft. Given that it is installed directly on the crankshaft, this device tends to increase the moment of inertia to be overcome at startup. Given that it constitutes the first filtering stage for engine torque fluctuations, the mechanism must be dimensioned with considerable inertia so that it has a significant effect, and the pivot-mounted modules that experience these non-attenuated fluctuations must themselves be particularly robust. An elevated primary inertia likewise results in an elevated inertia downstream from the inertial flywheel, at the friction clutch and at any filtering devices interposed between the clutch and the transmission; this conflicts with the objectives of reduced consumption and lighter-weight mechanisms.